Chemistry

Henderson–Hasselbalch Equation

Estimate buffer pH from a weak acid and its conjugate base.

pH ≃ p K_{a} + lo g_{10} (\frac{[ A ^{-} ]}{[ HA ]})

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Difficulty

Intermediate

Read time

3 min

Prerequisites

Algebra, logarithms, and molar quantities

Review statusNeeds review

Source

OpenStax, Chemistry 2e, §14.6

Adapted from Teng-Jui Lin’s CHEM 155 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Definition

Understanding the core concept

A buffer’s pH depends on the acid’s pK_a and the ratio of conjugate base to weak acid. Equal concentrations give pH approximately equal to pK_a under the dilute-solution approximation.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$pH$	Buffer pH	$1$
$p K_{a}$	Negative base-10 logarithm of the acid dissociation constant	$1$
$[A^{-}]$	Equilibrium conjugate-base concentration	$mol L^{- 1}$
$[HA]$	Equilibrium weak-acid concentration	$mol L^{- 1}$

Real-World Applications

Where this formula is used in practice

Buffer formulation

Estimate the conjugate-base ratio for a target pH.

Buffer composition

Relate composition changes to pH after any neutralization stoichiometry is completed.

Worked Example

Step-by-step calculation with real numbers

Problem

A buffer has pK_a = 4.76, equilibrium conjugate-base concentration 0.0200 mol/L, and weak-acid concentration 0.0100 mol/L. Estimate its pH.

Given

p K_{a} = 4.76

[A^{-}] = 0.0200 mol L^{- 1}

[HA] = 0.0100 mol L^{- 1}

Solution

pH ≃ p K_{a} + lo g_{10} (\frac{[ A ^{-} ]}{[ HA ]})

pH ≃ 4.76 + lo g_{10} (\frac{0.0200}{0.0100})

pH \approx 5.061

Final Answer

pH \approx 5.061

Formula Guide

Info

DifficultyIntermediate

Read Time3 min

PrerequisitesAlgebra, logarithms, and molar quantities

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, Chemistry 2e, §14.6

Adapted from Teng-Jui Lin’s CHEM 155 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Assumptions

• Both members of a weak conjugate acid–base pair must be present in appreciable amounts.
• Use equilibrium concentrations, or analytical concentrations only when their equilibrium changes are negligible; neglect activity corrections only when appropriate.

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